7. \( 3 \frac{2}{3}+2 \frac{3}{16}= \)

To solve \( 3 \frac{2}{3} + 2 \frac{3}{16} \), first convert the mixed numbers to improper fractions. For \( 3 \frac{2}{3} \): \( 3 \frac{2}{3} = \frac{11}{3} \) (since \( 3 \times 3 + 2 = 11 \)). For \( 2 \frac{3}{16} \): \( 2 \frac{3}{16} = \frac{35}{16} \) (since \( 2 \times 16 + 3 = 35 \)). Next, find a common denominator for \( \frac{11}{3} \) and \( \frac{35}{16} \). The least common denominator is 48. Convert \( \frac{11}{3} \): \( \frac{11}{3} = \frac{11 \times 16}{3 \times 16} = \frac{176}{48} \). Convert \( \frac{35}{16} \): \( \frac{35}{16} = \frac{35 \times 3}{16 \times 3} = \frac{105}{48} \). Now, add the fractions: \( \frac{176}{48} + \frac{105}{48} = \frac{281}{48} \). Finally, convert \( \frac{281}{48} \) back to a mixed number: \( 281 \div 48 = 5\) remainder \(41\), so \( \frac{281}{48} = 5 \frac{41}{48} \). Therefore, \( 3 \frac{2}{3} + 2 \frac{3}{16} = 5 \frac{41}{48} \).